is absolute vorticity, with ζ being relative vorticity, defined as the vertical component of the curl of the fluid velocity and f is the Coriolis parameter
f = 2Ωsinφ,
where Ω is the angular frequency of the planet's rotation (Ω=0.7272*10-4 s-1 for the earth) and φ is latitude.
In terms of relative vorticity, the equation can be rewritten as
where is the variation of the Coriolis parameter with distance y in the north-south direction and v is the component of velocity in this direction.
In 1950, Charney, Fjorloft, and von Neumann integrated this equation (with an added diffusion term on the RHS) on a computer for the first time, using an observed field of 500 mbgeopotential for the first timestep. This was the one of the first successful instances of numerical weather forecasting.
Vorticity is a mathematical concept used in fluid dynamics.
For any flow, you can write the equations of the flow in terms of vorticity rather than velocity by simply taking the curl of the flow equations that are framed in terms of velocity (may have to apply the 2nd Fundamental Theorem of Calculus to do this rigorously).
The barotropicvorticityequation is the simplest way for forecasting the movement of Rossby waves (that is, the troughs and ridges of 50 kPa geopotential) over a limited amount of time (a few days).
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